Tracing hierarchical galaxy formation with stellar

dynamics: From nuclei to halos

Loren Hoffman

Hebrew University of Jerusalem

UCSC, 8/17/2010

Dynamical imprint of galaxy formation

-Violent relaxation in mergers is incomplete (Lynden-Bell 1967).

-Memory of ICs encoded in integrals of motion (IOM).

-Time-dependence/perturbations -> diffusion in IOM phase space.

-Crossing of orbital boundaries -> erasure of ICs (relaxation).

-To understand galactic structure and evolution, need to identify macroscopic groups of orbits that conserve qualitatively similar IOM.

Stellar orbits are the building blocksof galaxies (images: Poon & Merritt 2001).

Orbital phase space need not beuniformly populated (image: van den Bosch et al. 2008).

Dynamical information in real galaxies

Image: http://seds.org/~spider/ngc/ngc.cgi?NGC4365

The stellar population of the NGC 4365 KDC is indistinguishable from that of the outer galaxy.NGC 4365: SAURON image

Gomez et al. 2010

Proctoret al. 2009

Binney & Tremaine 2008

Spherical potentials Axisymmetric potentials

-Energy, angular momentumconserved -> orbit confinedto plane

-Rosettes (precessing ellipses) uniformly fill annulus r0 < r < r1

over long times

-Centrifugal barrier shields star from center of potential

Box Inner long-axis tube Outer long-axis tubeShort-axis tube

3D triaxial potentials

Poon & Merritt 2001

Binney and Spergel 1982;figure from Hoffman et al. 2010

Imprint of orbitalstructure on kinematics

Origin of the orbital structure – effect of a CMC

Merritt &Valluri 1997

Kalapotharakoset al. 2004

Origin of the orbital structure

Hoffman et al. 2010

Hopkins et al. 2009

Hopkins et al. 2009

Barnes & Hernquist 1996,Hopkins et al. 2009

SAURON data

KDCs in 15-20% gas remnants

NGC4365 – van den Bosch et al. 2008

Hopkins et al. 2009:10% “extra light”componentin NGC 4365

NGC 4365 – comparison of 3D structure with simulations

Constraints from outer kinematics

Emsellem et al. 2004Proctor et al. 2009 Coccato et al. 2009

Outer kinematics II

Outerkinematics

III

NGC 5813

NGC 3414

NGC 5846

NGC 4486

Cappellari et al. 2007

Burkert et al. 2008The SAURON challenge

More general formation scenarios

Ceverino et al. 2009 Weil & Hernquist 1996

1) Complete exploration of merger phase space

2) Bulge formation throughClump migration in “wild disks”

3) Multiple mergers / cosmologically motivated sequences

Binary SMBHs in collisionless galactic nuclei

Requirements: Integrate cuspy system with N ≈ 107-8 for up to 500-1000 tdyn ;suppress relaxation enough to be in empty loss cone regime.

Ideal code: Pure triaxial NBSCF (no kicks) until initial spherical loss cone cleared out, switching to MCSCF after that.

(A)

1) O(N)2) Completely parallel3) No Cartesian

softening

The Self-consistent field (SCF) method

Most astrophysical systems modeled with N-body simulations undergo brief episodes of rapid evolution, long periods of slow evolution (tev >> tdyn).

(B)

Binary S/IMBHs in collisional nuclei

Milosavljevic & Merritt 2003Sharp phase space gradients near the loss cone.

Requirements: Integrate cuspy system with N ≈ 107 for up to 500-1000 tdyn ; suppress relaxation enough to be in empty loss cone regime and accurately treat 2-body relaxation.

Ideal code: Spherical, triaxial MCSCF with Henon kicks (note: unlike Spitzer MC, Henon method does not require a Maxwellian distribution!).

Relaxation in N-body simulations

Hernquist & Ostriker 1992

N = 2.5 x 103

Nmax = 6, lmax = 4

Evolution owing to time fluctuations of coefficients

Temporal smoothing

1) Initialize {mk, rk, vk}.2) Compute a(r) from eq’n (B).3) Integrate each particle’s orbit

separately through δt=εtrelax,.

4) Apply Henon kicks.5) Go back to step 2.

“Monte-Carlo” implementation

Energy conservation is currently an issue for long-term integrations of104– 105 dynamical times.

Suppressing relaxation with rare potential updates

Summary

-Merger model predicts a characteristic, physically intuitive orbital structure (though not necessarily unique), observable with SAURON + SMEAGOL

-Power of direct comparisons with dynamical models of observed systems: Physical intuition, some features detectable only this way

-Need for extension to more general formation models –cosmological merger trees, smooth/clumpy gas accretion, …

-SCF / MC technique ideal for studying nuclear kinematicsof SMBH binary nuclei; code under development.